Sum & Difference

Cosine sum and difference formula: cos(α ± β) = cos α cos β ∓ sin α sin β

cos(α±β)=cosαcosβsinαsinβ\cos(\alpha \pm \beta) = \cos\alpha \cos\beta \mp \sin\alpha \sin\beta

cos(α ± β) = cos α cos β ∓ sin α sin β. The signs are opposite: a plus inside gives a minus outside. That sign flip is the most commonly dropped detail in the whole topic, and it comes from cosine being even while sine is odd.

Related Sum & Difference identities

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Sum & Difference questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.